Weight painting deforms an object
The reason this happens is because you have animation information on the armature that you are painting to, the mesh updates to that information once it is painted to a certain bone.

This can be desirable if you have a certain pose that you do not know how it will deform the mesh, and you can weight paint until the mesh looks fine in the tricky position. However, this isn't the case, and we'll need to solve it.

Switch into pose mode. (Ctrl+Tab) now, hit A once or twice (depending) to select all of the bones. Alt+R will clear all rotation data, and likewise, Alt+G will clear translation data.

You may now weight paint without any mesh deformation.